Abstract
In this paper we propose a new gauge term in addition to the conventional gauge to acquire complete solution for the linear approximated gravitational equation. The calculation to make general form for the linear gravitational equation uses the well-known Nöether’s theorem saying that gauge symmetry is equal to conservation law. The unsolved coefficients in the equation require another condition which is leading to new gauge term. This proposed new gauge is a tensor product by a scalar quantity with a metric tensor having the trace value of 2. The scalar component in the 5th row and column of Kaluza-Klein’s metric tensor can be found as 2 diagonal components in our proposed 4×4 metric tensor. We also show that only a constant scalar gauge can be allowed in the curved space-time although arbitrary gauge can exist in the linear space-time.
Highlights
Long years ago, Kaluza and Klein proposed the initial unification theory of the electromagnetic force and gravitational force with their revolutionary 5-dimentional metric tensor
We have revealed that there is a gauge including a scalar quantity even in the four dimensions
We have found that the previously known vector gauge alone can not satisfy the law of conservation of symmetry in the linear approximated gravitational equation, and an additional gauge is needed
Summary
Kaluza and Klein proposed the initial unification theory of the electromagnetic force and gravitational force with their revolutionary 5-dimentional metric tensor. The first metric tensor proposed by Kaluza has a 5 × 5 structure and has a scalar component, k, in the 5th row and 5th column as can be seen in (1-1) [1] [2]. From the Kaluza-Klein theory, we have shown recently that gravity and electromagnetic force can be unified by using a gauge even with a 4 × 4 metric tensor [4] [5]. There is no gauge term with scalar component like “k” in the Kaluza-Klein metric tensor. We will first find out a field equation by using Nöether’s theorem [7] [8] (gauge symmetry and conservation) and conservation law in general electromagnetic fields, and extend to the gravitational field with a similar and consistent methodology
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of High Energy Physics, Gravitation and Cosmology
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
